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Question

In Young's double slit experiment, the source is red light of wavelength 7×107m. When a thin glass plate of refractive index 1.5 at this wavelength is put in the path of one of the interfering beams, the central bright fringe shifts by 103m to the position previously occupied by the 5th bright fringe. The thickness (inμm) of the plate is x. Find x.

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Solution

In Young's double slit experiment, if an object is put in the path of the beam then the shift in fringes is given by
shift=Dt(μ1)d
Also since the central bright fringe shifted to the position previously occupied by the 5th bright fringe, we have shift=5β
Dt(μ1)d=5β
t=5βdD(μ1)
We have fringe-width beta=Dλd
t=5λ(μ1)=5×7×107(1.51)
t=7μm

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